Hypothesis Testing Terms(cont Level of significance(a)-- a measure of confidence that can be placed in a result not merely being a matter of chance p value --The smallest level of significance at which you would reject H p-value in a right-tailed test p-value in a two-tailed test Robust System Design mit 人 16881 Session #7
Hypothesis Testing Terms (cont.) • Level of significance ( α) -- A measure of confidence that can be placed in a result not merely being a matter of chance • p value -- The smallest level of significance at which you would reject Ho Robust System Design 16.881 Session #7 MIT
C omparing the Variance of two samples Null hy hypothesis 0 2 Test statistic --F lVar(Ⅹ1) 2 Var(X2) Acceptance criteria-PPF(F, d1, d 2)-05< 1-a Assumes independence normal dist Robust System Design mit 人 16881 Session #7
Robust System Design 16.881 Session #7 MIT Comparing the Variance of Two Samples • Null Hypothesis -- Ho: • Test Statistic -- • Acceptance criteria -- • Assumes independence & normal dist. = r 2 1 σ σ F 1 r 2 Var ( X1 Var ( X2 . 2 1 ( , 1, 2) 0.5 −α pF F d d − < ) )
F Distribution Three arguments di (numerator doF) d2(denominator DOF) x(cutoff) d1 +d2 d1.d2 2 or x 十 F(x, dl, d2) Robust System Design mit 人 16881 Session #7
F Distribution • Three arguments – d1 (numerator DOF) – d2 (denominator DOF) – x (cutoff) F(x,d1,d2) Γ d1 d2 2 d1 d1 2 . d2 d2 2 . Γ d1 2 Γ d2 2 . x d1 2 1 d1 x. ( d2 d1 d2 2 . for x > 0 x ) Robust System Design 16.881 Session #7 MIT
Rolling dice Population 1-- roll one die Population 2-- roll two die Go to excel sheet dice f test.xls Robust System Design mit 人 16881 Session #7
Rolling Dice • Population 1 -- Roll one die • Population 2 -- Roll two die • Go to excel sheet “dice_f_test.xls” Robust System Design 16.881 Session #7 MIT